复杂网络引论 : 模型、结构与动力学

Part Ⅰ FUNDAMENTAL THEORY

1 Introduction

1.1 Background and Motivation

1.2 A Brief History of Complex Network Research

1.2.1 The Konigsburg Seven-Bridge Problem

1.2.2 Random Graph Theory

1.2.3 Small-World Experiments

1.2.4 Strengths of Weak Ties

1.2.5 Heterogeneity and the WWW

1.3 New Era of Complex-Network Studies

Exercises

References

2 Preliminaries

2.1 Elementary Graph Theory

2.1.1 Background

2.1.2 Basic Concepts

2.1.3 Adjacency Incidence and Laplacian Matrices

2.1.4 Degree Correlation and Assortativity

2.1.5 Some Basic Results on Graphs

2.1.6 Eulerian and Hamiltonian Graphs

2.1.7 Plane and Planar Graphs

2.1.8 Trees and Bipartite Graphs

2.1.9 Directed Graphs

2.1.10 Weighted Graphs

2.1.11 Some Applications

2.2 Elementary Probability and Statistics

2.2.1 Probability Preliminaries

2.2.2 Statistics Preliminaries

2.2.3 Law of Large Numbers and Central Limit Theorem

2.2.4 Markov Chains

2.3 Elementary Dynamical Systems Theory

2.3.1 Background and Morivation

2.3.2 Some Analytical Tools

2.3.3 Chaos in Nonlinear Systems

2.3.4 Kolmogorov-Sinai Entropy

2.3.5 Some Examples of Chaoric Sysrems

2.3.6 Stabilities of Nonlinear Systems

Exercises

References

3 Network Topologies： Basic Models and Properties

3.1 Introduction

3.2 Regular Networks

3.3 ER Random-Graph Model

3.4 Small-World Network Models

3.4.1 WS Small-World Nerwork Model

3.4.2 NW Small- World Network Model

3.4.3 Sratistical Properties of Small-World Network Models

3.5 Navigable Small-World Network Model

3.6 Scale-Free Network Models

3.6.1 BA Scale-Free Network Model

3.6.2 Robustness versus Fragiliry

3.6.3 Modified BA Models

3.6.4 A Simple Model with Power-Law Deg-ree Distribution

3.6.5 Local- World and Multi-Local- Wortd Network Models

Exercises

References

Part Ⅱ APPLICATIONS-SELECTED TOPICS

4 Internet： Topology and Modeling

4.1 Introduction

4.2 Topological Properties of the Internet

4.2.1 Power-Low Node-Degree Distribution

4.2.2 Hierarchical Structure

4.2.3 Rich-Club Structure

4.2.4 Disassortative Property

4.2.5 Coreness and Betweenness

4.2.6 Growrh of the Internet

4.2.7 Router-Level Internet Topology

4.2.8 Geographic Layout of the Interner

4.3 Random-Graph Network Topology Generator

4.4 Structural Network Topology Generators

4.4.1 Tiers Topology Generaror

4.4.2 Transir-Stub Topology Generator

4.5 Connectivity-Based Network Topology Generators

4.5.1 Inet

4.5.2 BRITE Model

4.5.3 GLP Model

4.5.4 PFP Model

4.5.5 TANG Model

Index

《复杂网络引论：模型、结构与动力学（第二版 英文版）》是为自然科学、数学和工程领域的研究生以及本科高年级学生编写的-本入门教科书，在第一版的基础上补充、修订而成，可以作为一个学期教学使用的讲义，也可以作为科研参考书或自学读物。
　　《复杂网络引论：模型、结构与动力学（第二版 英文版）》包括两大部分内容：第一部分是基础理论，包括背景材料和信息并附有适量的练习题，旨在让读者熟悉一些最基本的建模方法和分析技巧。第二部分是应用选题，包括复杂网络在几个代表性领域中的应用研究，这些章节彼此相对独立。最后一章是近年来比较活跃的几个前沿研究课题的简介。各章均附有详细的关键文献，以帮助有兴趣的读者能够很快地进入这些研究领域。
　　《复杂网络引论：模型、结构与动力学（第二版 英文版）》保持了第一版的特色，通俗易懂，侧重于主要思想和基本方法的介绍，具有初等微积分、线性代数和常微分方程的读者能够轻松地学习书中的主要内容。同时增加了部分新内容，包括基本数理统计和动力系统基础、网络社团结构、网络博弈等。